Similarly, the people who will survive the coming climate catastrophes may well live better lives than we do today, and thus some future Economist may well claim that it all turned out OK in the end. But that analysis ignores the billions of people whose lives will likely end because of global warming.
...that number is not even remotely plausible. Where did you get billions from?
Example: 250,000 extra deaths estimated between 2030 and 2050. That means an extra 5 million deaths in that period (https://www.who.int/news-room/fact-sheets/detail/climate-cha...).
Another: 83 million extra deaths by 2100, and I suspect that's under the more pessimistic scenario (https://www.forbes.com/sites/dishashetty/2021/07/30/climate-...)
Action on climate change is very slow, but happening. Climate change is not going to be even remotely as close to as bad as you appear to think it will be.
* Health/medical technology and access
* Abundance and variety of food
* Education
* Life expectancy
* Quality (in terms of health) of life
* Child mortality
Looking at life expectancy alone, I'd be surprised if their life expectancy was higher (is this what you had in mind? https://sc.edu/uofsc/announcements/2014/05_sharondewitte_bla...). Certainly some individuals would live longer lives than some individuals, but I wouldn't expect the life expectancy to be higher, nor would I expect the quality of health of that life to be better.
In some ways I could imagine they'd be better -- e.g., amount of land they could own. If you have some data or information about their life quality, I would be interested in seeing it.
Regarding Rawls' veil, I did say, and do think, that we should be ensuring that everyone gets brought along. For someone who isn't convinced about that, the veil may be a good thought experiment to help them along.